A model of interaction of a vertical flow of compressible gas with a particle (Q2753425)

A system of differential equations describing levitation of a particle in vertical gas flow is suggested. This system expresses (i) the equation of force balance acting on the particle and (ii) the dependence reflecting the variation of gas mass under the particle occurring due to pressure change in this section, and also the volume under the particle during its motion. A theoretical dependence between the mass consumption of the bearing gas and pressure and the relationship between state parameters of ideal gas under adiabatic conditions are used to complete the governing system of equations. The resulting nonlinear system was solved by Runge-Kutta method. Examples of typical dependence for gas pressure, coordinate and velocity of the particle are presented. The suggested theory enables one to explain some already known experimental results.